Skip to main content
SpringerLink
Log in

Solutions for a system of nonlinear random integral and differential equations

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper, we first prove a Darbao type fixed point theorem for a system of continuous random operators with random domains. Then, by using the theorem, we give the existence criteria of solutions for a systems of nonlinear random Volterra integral equations and for the Cauchy problem of a system of nonlinear random differential equations. The existence of extremal random solutions and random comparison results for these systems of random equations are also obtained. Our theorems improve and generalize the corresponding results of Vaughn, Lakshmikantham, Lakshmikantham-Leela, De Blasi-Myjak and Ding.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. T. Bharucha-Reid, Random Integral Equations, Acad. Press, New York (1972).

    Google Scholar 

  2. V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, New York (1981).

    Google Scholar 

  3. C. J. Tsokos and W. J. Padgett, Random Integral Equations with Applications to Life Science and Engineering, Acad. Press, New York (1974).

    Google Scholar 

  4. Ding Xieping, Criteria for the existence of solutions to random integral and differential equations, Appl. Math. and Mech. (English Ed.), 6, 3 (1985), 269–275.

    Google Scholar 

  5. Ding Xieping, Existence and comparison results for random integral and differential equations, Appl: Math. and Mech. (English Ed.), 7, 7 (1986), 643–650.

    Google Scholar 

  6. R. L. Vaughn, Existence and comparison results for nonlinear Volterra integral equations in Banach spaces, Appl. Anal., 7 (1978), 337–348.

    Google Scholar 

  7. R. L. Vaughn, Criteria for the existence and comparison of solutions to nonlinear Volterra integral equations in Banach spaces, Nonlinear Equations in Abstract Spaces, Acad. Press, New York (1978), 463–468.

    Google Scholar 

  8. V. Lakshmikantham, Existence and comparison results for Volterra integral equations, Volterral Integral Equations, Springer-Verlag, 737 (1979), 120–126.

    Google Scholar 

  9. F. S. De Blasi and J. Myjak, Random differential equations on closed subsets of Banach spaces, J. Math. Anal. Appl., 90 (1982), 273–285.

    Google Scholar 

  10. Ding Xieping, Fixed point theorems of random set-valued mappings and their applications, Appl. Math. and Mech. (English Ed.), 5, 4 (1984), 1529–1542.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, 610066, Chengdu, P. R. China

    Ding Xieping

  2. Department of Mathematics, Nantong Teacher's College, 226007, Nantong, P. R. China

    Wang Fan

Authors
  1. Ding Xieping
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported by the National Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xieping, D., Fan, W. Solutions for a system of nonlinear random integral and differential equations. Appl Math Mech 17, 495–506 (1996). https://doi.org/10.1007/BF00119746

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00119746

Key words

Search

Navigation